Let $X_{ij} \, 1\leq i\leq m, 1\leq j \leq n$ are uniform random variables (firstly assume them distributed on [0,1]), I want to know the pdf, mean and variance of $\sum_{j=1}^n log(\sum_{i=1}^m X_{ij})$, what if $X_{ij}\sim U(a_i,b_i)$?I have no idea. Please help me. Thanks a lot!

ps:see https://arxiv.org/pdf/math/0411298v1.pdf for results of sum of non-identical uniform variables $U(c_i-a_i,c_i+a_i)$.

  • $\begingroup$ What is your personal work on the subject ? Do you know for example that for $n=1$ you have an exponential distribution ? What happens for $n=2$ ? Have you tried to simulate the law on a computer ? etc... Work hard on a question, then explain where you are blocked. $\endgroup$ – Jean Marie Mar 16 at 7:07

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